This is a 3 by 3 game. Two oligopolists Proctor & Gambling (PG) and Johnson & Jo

Question

This is a 3 by 3 game. Two oligopolists Proctor & Gambling (PG) and Johnson & Johnson (JJ) and three advertising strategies (High ads cost, Medium or Low for each), which produces nine scenarios. Ties are a possibility (two equally desired results). Answer the following questions: Only one of the two oligopolists has a dominant strategy, which Oligopolist? And what is his/her dominant strategy? Identify any Nash equilibrium, if any exist? If this was a cartel - where they co-decide their strategies - It is not difficult to see what their preferred cell would be. What cell do you think they will end up choosing together? Why?

Explanation / Answer

For PG,

If JJ plays high cost, it will play low

If JJ plays medium, it will play low

If JJ plays low, it will play medium

So there is no dominant strategy for PG. Dominant strategy is which a player plays irrespective of the move by the other player.

For JJ,

If PG plays high, it will play low

If PG plays medium, it will play low.

If PG plays low, it will play low

Thus for JJ, playing low is the dominant strategy as it should play low cost strategy irrespective of the PG's move.

b) Nash equilibrium is thus to play 'low' by both players as no player will have an incentive to shift from this strategy.

c) If it is a cartel, they will both prefer low cost as it will maximize their joint profit.

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